论文标题
玻色子bogoliubov-de Gennes系统的拓扑不变
Topological Invariant for Bosonic Bogoliubov-de Gennes Systems with Disorder
论文作者
论文摘要
使用非交通性几何形状的方法，我们定义了具有独特的数学特性的骨气型bogoliubov-de Gennes系统中的拓扑不变的 - 非热性。为了证明定义的有效性，我们在数值上研究了一个二维的无序人造自旋冰模型。在干净的限制中，我们澄清拓扑指数与Chern数字完全一致。我们还表明，拓扑指数对疾病是可靠的。该公式提供了巨大的局部局部局部定位，提供了Magnon Hall制度中的拓扑索引$ n _ {\ rm ch} = 1 $，$ n _ {\ rm ch} = 0 $。我们还以示例表明我们的方法可以扩展到其他对称类。我们的结果为对有疾病的拓扑授权系统的进一步研究铺平了道路。
Using the method of noncommutative geometry, we define a topological invariant in disordered bosonic Bogoliubov-de Gennes systems, which possess a unique mathematical property---non-Hermiticity. To demonstrate the validity of the definition, we investigate a disordered artificial spin ice model in two dimensions numerically. In the clean limit, we clarify that the topological index perfectly coincides with the Chern number. We also show that the topological index is robust against disorder. The formula provides the topological index $n_{\rm Ch}=1$ in the magnon Hall regime and $n_{\rm Ch}=0$ in a trivial localized one. We also show by example that our method can be extended to other symmetry classes. Our results pave the way for further studies on topological bosonic systems with disorder.
